Would a hollow metal sphere with a vacuum inside float?

30 May 2010

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Question

Would it be possible to make a hollow metallic sphere float if you suck out all of the air and create a vacuum inside?

Answer

We asked Dominic Ford from Naked Astronomy.

Dominic - Yes, it certainly would be. What's important is whether the average density of the sphere plus whatever is inside it is greater or less than the density of the water that it will be floating in. So for example, a ship floats because although a ship is made of steel and that's very heavy, it's got air in there as well and the air is much less dense than the water it's floating in, so a ship as a whole floats. Now if you take a sphere, the metal outside of the sphere will be much heavier than the water, but because it hasn't got anything in it, that doesn't contribute to the density. So its average density be quite low. So it will float. It will actually float better than if you filled it with hydrogen or helium which, although they are lighter than air, they still have some mass to them, more than the mass of the vacuum which is nothing at all.

Chris - Indeed. It's a good party question that, isn't it? Which is going to float more, a sealed barrel full of air, a sealed barrel full of hydrogen, or a barrel with a vacuum, and that most people will go for the hydrogen and actually, it's the vacuum that floats the best.

Dominic - Yes, of course. You don't see barrels filled with vacuums very often because it's so hard to suck air out of a barrel!

Comments

So I just did my own research and calculations, and given that a Boeing 747 weighs approximately 368 tons, the amount of pure-zero air displacement (as afforded by a vacuum) necessary to reach a weight of zero would be an astonishing 9.21 mil cu ft. The goal doesn't have to be zero, however, but rather just a significant reduction in weight overall. Still, given that total weight, it seems unlikely that any implementation of vacuum technology in commercial aircraft would be able to make a noticeable impact without a significant redesign, likely eschewing all currently-used materials, such as steel, in favor of much lighter materials. Perhaps we will be at a place in the future where carbon nanotubes or some yet undiscovered material is able to bridge the gap between thought experiment and reality with regard to the feasibility of such a technology.

The answers above reflect my own suspicion, but it makes me wonder if a large enough vessel, made of a light enough material, containing a vacuum within, would float in air. For instance, if you made a thin-walled rigid plastic sphere, weighing less than 0.08 lbs and of a volume greater than 1 cu ft, would it float away? As air weighs approximately 0.08 lbs/cu ft, logic would seem to dictate so, yet this seems like it shouldn't be possible. Is there some rule of physics which says that any known earth material constructed at the necessary dimensions to inhabit a large enough volume at a low enough mass to float in air would necessary be too fragile to support the vacuum within? If not, it seems like it would be useful to incorporate such devices into aircraft in order to reduce fuel costs. Imagine a passenger liner whose wings, tail, fuselage walls, and nose weigh less than air, such that the entire vessel's weight is reduced and therefor requires less energy (i.e. fuel) to achieve and maintain flight.

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